Drag cars need ALL the side wall they can get, to flex on take-off and gain "off the line" traction. Getting them to turn a corner, at speed, is another story.
Race cars that use 15" or 16" rims still have a low profile tyres, with thick side-walls, to help cornering. Smaller rims with low profile tyres equates to a smaller rolling diameter: faster acceleration, better braking and better handling.
Rev210: If you know anyone that runs 255 with 40 profile, on a 18" rim, smack 'em in the back of the head . I think 18x30x255 is recommended, at worst 18x35x255.
Believe it or not; 16" rims with tyres, generally have the same rolling diameter as 18" rims with tyres. You have alot more side-wall flex with 16" tyres, thus resulting in a degraded performance. The extra rubber on a 16" tyre will almost equate to the same weight as the extra alloy on a top quality 18" forged rim. But if you go wider you are also getting more rubber and alloy.
Bottom line: If you are concerned about performance and handling, spend at least $3k on top forged rims and another $3K on good quality rubber. This only really applies to about 5% of enthusiests, as the rest of us will never really justify the differance.